Jupiter's Moons and the Longitude Problem

May-June 2002, Mercury Magazine, pp. 34-39
by Robert Mentzer

For a period lasting over a century, the most effective
way to determine longitude was to observe the Galilean
moons of Jupiter.

On July 15, 1806, Captain Zebulon Pike led
a party of 23 soldiers and 51 Amerindians
westward out of St. Louis, Missouri. One of
Captain Pike's assignments was to escort the
Amerindians back to their villages. He was
then to continue on and explore the southwestern
part of Thomas Jefferson's new Louisiana Purchase.
On this very day, Meriwether Lewis and William
Clark were near the Great Falls of the Missouri
River (in Montana) on the last leg of their
return journey, which would end in September.
They had been sent to explore the rich furtrapping
areas of the northern part of the purchase.
Later in his expedition, Pike traveled to
eastern Colorado and described a mountain
that now bears his name, Pike's Peak.

On August 23, 1806, Pike camped with the
Osage Amerindians in their villages near the
Kansas-Missouri border. On that day he wrote
in his journal, "Took equal altitudes
and a meridional altitude of the Sun, but
owing to flying clouds, missed the immersion
of Jupiter's satellites." In the middle
of what Pike would later call "the great
American Desert," surrounded by hostile
Amerindians, hundreds of kilometers from civilization,
he was looking through a telescope. Isn't
this rather strange behavior for a rugged
adventurer? Actually no, for Pike was doing
what explorers had been doing for more than
a century: He was using Jupiter's moons to
determine his longitude.
Longing for Longitude

It's easy to find one's latitude by measuring
the altitude of the North Star (Polaris).
Alternatively, one can measure the peak height
of the noon Sun, or of a star after dark,
and then find the latitude from a set of tables.
Longitude, on the other hand, is much more
difficult to determine.

Being at 40° north latitude means you
are somewhere on a circle that runs around
the world 40° north of the equator. But
where on that circle are you? Polaris will
appear 40° above the northern horizon
on any location on that circle and the Sun's
peak altitude will be the same. The only difference
will be that the Sun will peak at different
times at different points on the circle as
Earth rotates. So time is the key to finding
longitude. Tables can tell you when the Sun
or certain stars will peak over Greenwich,
England. It takes Earth 24 hours to complete
one 360° rotation, so Earth turns 15° per
hour. If you have an accurate clock set to
Greenwich time, and the Sun peaks an hour
later at your location than the table says
it peaks in Greenwich, you are one hour (or
15°) west of Greenwich. Given an accurate
clock, you can easily determine longitude.
But prior to about 1770, clocks were not accurate
enough to determine longitude. Travelers could only
make crude estimates of their longitude. This was
a real concern for sailing ships, which were constantly
in danger of running aground because of poor longitude
estimates. In 1707 a British fleet approaching the
southern coast of England (commanded by Sir Clowdisley
Shovell) ran aground on the Scilly Islands during
a storm, with the loss of 2,000 lives. Those 2,000
deaths in the England of 1707 were equivalent to
about 60,000 deaths in today's America. Imagine the
shock if 300 commercial jets crashed in one day.
Almost every person would know a victim. The public
outcry in England forced the Admiralty to offer a
prize of 20,000 pounds, a fortune at the time, to
anyone who could solve the longitude problem.

To win the Admiralty's prize, one had to
determine longitude to within half a degree
after a long ocean voyage. At the equator,
Earth's circumference is about 40,000 kilometers
(24,900 miles) and the Sun takes 24 hours
to circle. So the Sun appears to move at 1,670
kilometers (1,040 miles) per hour, or 15° per
hour (10 in 4 minutes). To win the prize,
the clock had to be within half a degree (or
2 minutes) of the correct time. Any clock
that loses one second a day for a year would
be off by 365 seconds, or 6 minutes. In 1707,
no clock in the world came anywhere near the
required accuracy.

A century earlier Galileo had to use crude
water clocks for his work on falling objects.
But he made two key suggestions that were
of tremendous help in solving the longitude
problem. The first was his observation that
a pendulum could be used as a clock. By 1660
Dutch astronomer Christian Huygens had perfected
the pendulum clock. But pendulum clocks that
kept excellent time when hanging on a motionless
wall were hopelessly inaccurate when carried
over rough terrain or on a pitching ship.

[This world map from 1713 is a reproduction
of Giovanni Domenico Cassini's 1696 map, which
was the first world map created with accurate
longitude measurements from the observations
of Jupiter's moons. Inscriptions are written
in French and Latin. Courtesy of the Serge
A. Sauer Map Library, University of Western
Ontario.]

A Heavenly Clock
It was Galileo's second idea that led to a successful
method of determining longitude. In 1609-1610 Galileo
had used his new telescope to discover four moons
circling Jupiter (later named lo, Europa, Ganymede,
and Callisto). Galileo quickly realized that the
steady procession of circling moons was a heavenly
clock that could be seen from anywhere on Earth
whenever Jupiter was in the night sky.

A good mathematician could take observations
of the eclipses of the moons and predict the
times of future eclipses. An observer anywhere
on Earth would look at tables to see if any
eclipses occurred that day or in the next
few days. The observer would pick some likely
eclipses based on estimates of one's longitude.
The observer would look at Jupiter, identify
the moons, and watch an eclipse. The observer
could then set his or her clock to the listed
Greenwich time for that eclipse.

An extremely accurate clock was no longer
needed. With the clock now set correctly to
Greenwich time, in the next few days one would
measure the time when the noon Sun peaked.
The observer would then compare this time
with the Greenwich time listed in the almanac.
If the Sun peaked 5 hours later than the table
said it would, the longitude would be 5 hours
times 15° per hour, or 75° west of
Greenwich. And that is exactly why Zebulon
Pike was observing Jupiter's moons from that
lonely Kansas prairie in 1806.

Pike didn't use Galileo's tables because
Galileo was never able to calculate the eclipses
accurately enough. That honor fell to Italian-born
astronomer Giovanni Domenico Cassini, who
published an improved set of tables in 1668.
Cassini had emigrated to France after King
Louis XIV had formed the Royal Academy of
Science. The king wanted to make France the
world leader in science, so he was recruiting
the world's best scientists. Cassini's work
was perfect for another of the Academy's projects,
the accurate mapping of France. This endeavor
required the determination of longitude, the
very thing that Cassini's work promised to
do with unsurpassed accuracy. So the king
made Cassini an offer he couldn't refuse.

Cassini's team traveled to the major cities
of France and with its telescopes observed
an eclipse of one of Jupiter's moons. This
enabled the team to set its clocks to the
correct reference time. The next day the team
members would time when the Sun peaked. If
it peaked one-tenth of an hour later than
the time the tables listed for Paris, they
were one-tenth of 15° (1.5°) west
of Paris. With the Sun moving at about 1,600
kilometers (1,000 miles) an hour, this placed
the city 160 kilometers (100 miles) west of
Paris.

["I pay my astronomers well and they
have diminished my kingdom." - King Louis
XIV]

The results were revelatory. It was only
a few hundred miles from Paris to the coastal
cities over roads that had been trodden by
Roman engineers and countless Frenchmen. Yet
these cities were actually up to 100 kilometers
(60 miles) closer to Paris than the old maps
had indicated. This was a huge error, which
exposed the inaccuracies in the older methods.
King Louis is rumored to have said, "I
pay my astronomers well and they have diminished
my kingdom."

Having mapped France, Cassini and his team
moved on to do the world. France was in an
expansionist phase and her explorers were
everywhere, closely followed by her Jesuit
priests. Cassini began to train mathematically
minded young priests. When they reached their
assigned destinations, they measured the latitude
and longitude and sent the results back to
Paris.

Meanwhile, Cassini began to lay out a huge
circular map on the third floor of the Observatoire
de Paris. A circle about 10 meters in diameter
was drawn on the floor with the North Pole
at the center. As longitude from around the
world were reported, thee e crc added to this
map. Cities and farflung locales such as Québec,
Santiago, Lisbon, Venice, Cairo, Siam, India,
Canton, and Peking were added. The first accurate
map of the world slowly took shape. In 1696
Cassini published his new map, the first ever
to use Jupiter's moons to determine longitude.
The era of truly accurate maps had arrived.
More than a century later, Zebulon Pike's
observations went into improved maps of the
American West.

Problems at Sea
But a technique that worked well on land was hopeless
at sea. No one standing on the moving deck of a
ship could possibly keep a telescope trained on
those tiny moons of Jupiter, so the Admiralty continued
to search for a suitable method of determining
longitude. In 1775 Captain Cook returned from his
second voyage singing the praises of an amazing
chronometer built by John Harrison, which easily
met the requirements for the Longitude Prize.

Harrison was an English clockmaker who devoted
his life to perfecting a clock that could
win the prize (Dava Sobel describes his trials
and tribulations in her excellent book Longitude).
One of Harrison's sea trials was a trip to
the Caribbean, where the chronometer's prediction
of longitude was checked by observations of
Jupiter's moons.

After a century of being the only accurate
method of determining longitude, Jupiter's
moons had a serious rival. In fact, it had
two rivals. Britain's Astronomer Royal, Nevil
Maskelyne, had introduced a method called "lunar
distances," which used the Moon's motion
against the backdrop of fixed stars. In principle
this was the same as using the motions of
Jupiter's moons around Jupiter. But the technique
was very complicated, requiring three measurements
of angles in the sky as close together in
time as possible along with at least 30 minutes
of calculations. Its advantage was that the
Moon wasn't hidden in the Sun's glare as often
as Jupiter was. Eventually, the chronometer
method would prevail. It was the simplest
and it could he used on days when the Sun
or clouds interfered with measurements of
the Moon or Jupiter.

Jupiter's moons and their shadows routinely
cross the planet's face from our point of
view. This is because we're viewing Jupiter
and its moons along the Jovian system's orbital
plane. Such crossings are called transits.
lo transits every 1.77 days, while Europa
traverses every 3.55 days. It's 7.15 days
between transits for more distant Ganymede
and 16.69 days between transits for Callisto,
when transits happen at all.

A 6-inch or larger backyard telescope working
at 200 power will show transiting moons as
disks against Jupiter's face. b's disk appears
grayish on Jupiter's cloudtops, while Europa
is very light and often difficult to recognize,
especially when it lies in front of a bright
hand in Jupiter's atmosphere. Ganymede and
Callisto appear somewhat darker, so they are
usually easy to see. The best time to spot
a transiting moon is just as it enters or
leaves Jupiter's disk. A moon's disk stands
out more visibly against Jupiter's edge (limb),
which is darkened because of the effects of
our looking through a thicker cross section
of the planet's atmosphere.
Transits of moon shadows are even easier to spot.
There's no mistaking a black dot-like impression
on Jupiter's cloudtops. Before Jupiter reaches opposition,
shadows creep onto the planet's disk before the satellite
begins its transit. After opposition, the satellite
goes first. In the case of Ganymede and Callisto,
several hours can elapse between the time when a
satellite first transits and when its shadow appears.

Periodically, Jupiter eclipses each of the
four large moons as they pass into the planet's
mammoth shadow. In a telescope, a moon's brightness
takes several minutes to fade to black as
it enters the shadow. Reappearances are just
as gradual.

When Earth passes directly between Jupiter
and the Sun (meaning Jupiter comes to opposition),
as it did last December 31, Jupiter's shadow
falls directly behind the planet. (Next year's
opposition is February 2.) But the viewing
geometry changes just a bit during the months
leading up to and away from opposition. Our
perspective allows us to peer slightly around
the left or right side of Jupiter and look
down this shaft of darkness.

This May and June, the shadow projects from
behind the planet's left, or east, side. After
Jupiter passes behind the Sun on July 20 and
emerges into the morning sky, we'll be looking
in on the shadow emerging from the planet's
right, or western, limb.

Io orbits so close to Jupiter that, depending
upon our viewing perspective, we see it either
entering or exiting Jupiter's shadow. We never
see both on the same evening. This is because
Jupiter's disk almost entirely obscures our
view of the planet's shadow at b's distance
from Jupiter. After opposition, we always
see lo disappear behind the limb of Jupiter
and then reappear from the planet's shadow.
Conversely, before opposition we always see
lo disappear into the shadow and later reappear
from behind the disk.

The same largely holds true for Europa. Ganymede
and Callisto, however, are far enough from
Jupiter so that we see both entry into and
exit out of eclipses, except at times near
opposition. Eclipse lengths vary because these
moons don't always pass through the middle
of Jupiter's shadow: Ganymede averages 3.25
hours, while Callisto takes about 4 hours.

Because of a combination of Sun angles (because of the slight tilt of
Jupiter's axis to its orbit) and Callisto's distance from Jupiter, Callisto
misses Jupiter's shadow entirely for 3 years at a time. Callisto entered
its most recent eclipse season late last year and will regularly pass
through Jupiter's shadow on each orbit until about 2004.

Jupiter's moons still had some advantages, so this method would not die
easily. Zebulon Pike's 1806 expedition couldn't afford a chronometer even
if one had been available in St. Louis. In addition, the lunar distance
method was so difficult that Pike went with the old but reliable method
of observing Jupiter's moons. Three years earlier, Lewis and Clark's well-financed
expedition had carried a chronometer purchased in Philadelphia and equipment
for using the lunar distance method, which Thomas Jefferson favored. A
few months into the trip the chronometer stopped.

Chronometers, which worked fine when kept
in a special case in the captain's cabin,
could not take the pounding of a long trip
on a packhorse or the rocking of a canoe on
a wild river. These were delicate scientific
instruments; if you gave them a licking they
stopped ticking. So the situation had just
reversed. Jupiter's moons worked fine on land
but not on a ship. Chronometers worked fine
on ships, but they couldn't hold up during
extended journeys across land.

Clark reset his chronometer with the lunar
distance method whenever it stopped, but with
only a few weeks of training in the technique,
his results were disappointing. Ferdinand
Hassler, the West Point mathematician who
was given the observations, was reported by
Jefferson in 1817 to have "given up the
calculations in despair:'

In 1832 Captain Benjamin Bonneville used
Jupiter's moons to determine his longitude
on his western expedition. John Fremont's
western expeditions of 1842-44 carried multiple
chronometers, all of which broke or ran erratically.
Fremont eventually used Jupiter's moons to
determine his longitude. But these were last
gasps of a dying system. Chronometers were
getting better, and this improvement, along
with the ability to send time signals by telegraph,
led to the demise of the Jupiter moons system.
Thus a method that produced the first accurate
maps, a method that was the only accurate
way to determine longitude for 100 years,
and which played an important role for another
70 years, fell by the wayside of scientific
progress.

The moons of Jupiter still endlessly circle
the giant planet, and Jupiter still shines
down upon us as it has through the ages. So
next time you are out on a starry night and
look up and see Jupiter, take a moment to
think of Galileo, Cassini, the Jesuit priests,
Zebulon Pike, John Fremont, and all the others
who gazed across 600 million kilometers into
the blackness of space in order to determine
just where they stood on this green Earth.

Retired physics and astronomy teacher ROBERT
MENTZER (robmentzer@comcast.net) is treasurer
of the Delaware Astronomical Society. One
of his hobbies is reading about the early
exploration of the West. When he came across
references to Jupiter's moons in both Pike's
and Fremont's journals, he had to
find out more. This article is the result.

-----Chronometers were delicate scientific
instruments; if you gave them a licking they
stopped ticking.-----

Determine Your Longitude with Jupiter's Moons
by Morris Jones

It was MIT physicist Philip Morrison who
taught me, in a television documentary, how
to use Jupiter's moons as a system for synchronizing
clocks. This is the first step in calculating
longitude with astronomical observations.
With an ephemeris for Jupiter satellite transits
and occultations that is accurate for the
time at the Royal Greenwich Observatory, you
can synchronize your clock to the observatory's
by watching the scheduled event. The difference
between your local time and Greenwich local
time reveals your longitude.

On a clear night in late February, I decided
to try this experiment. I set up my 4-inch
refractor on my back deck outside my house
in San Rafael, California. My favorite Jupiter
ephemeris (www.projectpluto.com/ jevent.htm)
predicted an occultation of Europa for 0510
Greenwich Mean Time (GMT) the following day,
or 9:10 p.m. Pacific Standard Time, my local "standard" clock.
This event provided a splendid opportunity
to synchronize my own GMT clock.

These days it's easy to set your watch to
GMT. My computer stays synchronized to a variety
of reference clocks available on the Internet
using the network time protocol (NTP). So
I already knew that my watch was correct.

At about 8:40 p.m., I had my mount aligned
and tracking, and Jupiter was looking big
and beautiful. I wanted to test my ability
to judge the precise moment when the occultation
was complete, so I stopped looking at my watch.
I knew it was several minutes before the ephemeris's
predicted time when I first saw Europa brushing
against Jupiter's limb. It was like watching
a very distant sunset as Europa sank farther
behind Jupiter's disk, appearing as a tiny
lump on the edge. The lump shrank to a smaller
dot, but it was still there. Would I be able
to tell the exact moment of occultation? I
looked again and couldn't see Europa. "But
wait' I thought, "there's still a tiny
pinpoint on the edge. Or is it just my imagination?"

Finally it was clear that nothing was left.
No odd pinpoints appeared even when I used
averted vision. It was time. I looked at my
watch. It was 9:10:30 - dead center in the
designated minute.

Following through with the experiment, now
that I had a clock synchronized to GMT, I
could calculate the sidereal time at Greenwich.
Sidereal time, the right ascension coordinate
crossing overhead at any particular moment,
is the key to calculating longitude. Longitude
is simply the difference between the sidereal
time at a reference location (Greenwich) and
the local sidereal time, expressed as degrees
instead of hours, minutes, and seconds.

But my experiment was missing a crucial piece
of equipment that a 19thcentury surveyor would
have had: a transit scope. A transit scope
points only along the meridian. The mount
would be plumbed to vertical, and aligned
very carefully with the north celestial pole.
I could approximate a transit scope by turning
off my mount's clock drive and reorienting
the mount so the telescope is constrained
to rotate along a line including the zenith
and the north celestial pole. Alas, most telescope
mounts, mine included, won't twist into such
a configuration.

If I had such a device, I could watch for
any charted star to cross my local meridian.
At that moment, my local sidereal time would
match the right ascension of that star. I
would consult my recently synchronized GMT
clock and convert that time to the Greenwich
sidereal time, using published tables. Take
the difference between local sidereal time
and Greenwich sidereal time, convert it to
degrees, and bingo! Longitude.

MORRIS JONES (www.whiteoaks.com)
serves as newsletter editor for the San Jose Astronomical Association.
He is also an avid member of the San Francisco Sidewalk Astronomers.